[15] **viXra:1909.0603 [pdf]**
*submitted on 2019-09-29 14:48:48*

**Authors:** Andrei Lucian Dragoi

**Comments:** 6 Pages.

This paper proposes two distinct types of imaginary (im) infinities ("imfinities") in mathematics and meta-mathematics (including meta-geometry), emphasizing the unlimited "diversity" of zero and infinity, with far-reaching implications in all these domains, but also in math-related domains like modern physics, including the help in redefining the basics of Einstein's General relativity theory (GRT), quantum field theory (QFT), superstring theories (SSTs) and M-theory (MT).
Keywords (including a list of main abbreviations): imaginary (im) infinities (“imfinities”), mathematics, metamathematics, metageometry, zero, infinity; Einstein’s General relativity theory (GRT); quantum field theory (QFT); superstring theories (SSTs); M-theory (MT);

**Category:** General Mathematics

[14] **viXra:1909.0550 [pdf]**
*submitted on 2019-09-25 13:28:46*

**Authors:** A.I.Somsikov

**Comments:** 4 Pages. -

The description of the complex number which is not containing a concept of the complex
plane is offered.

**Category:** General Mathematics

[13] **viXra:1909.0537 [pdf]**
*submitted on 2019-09-24 07:30:46*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

We give some representations of Pi.

**Category:** General Mathematics

[12] **viXra:1909.0536 [pdf]**
*submitted on 2019-09-24 07:33:18*

**Authors:** Edgar Valdebenito

**Comments:** 1 Page.

This note presents two formulas.

**Category:** General Mathematics

[11] **viXra:1909.0535 [pdf]**
*submitted on 2019-09-24 07:35:55*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

Numerical evaluation of the integral: int(f(x),x=0..1)=pi/2

**Category:** General Mathematics

[10] **viXra:1909.0517 [pdf]**
*submitted on 2019-09-24 16:12:58*

**Authors:** Saburou Saitoh

**Comments:** This version was written for the Proceedings of ICRAMA2019 (16-18 July, 2019) with the 8 pages restriction under the requested form.

Based on the preprint survey paper, we will introduce the importance of the division by zero and its great impact to elementary mathematics and mathematical sciences for some general people. For this purpose, we will give its global viewpoint in a self-contained manner by using the related references.
This version was written for the Proceedings of ICRAMA2019 (16-18 July, 2019) with the 8 pages restriction under the requested form.

**Category:** General Mathematics

[9] **viXra:1909.0483 [pdf]**
*replaced on 2019-09-29 20:36:38*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 5 Pages.

This tutorial parlays two determining properties of positive-integer power functions of a positive real variable into closed formulas for the real power functions of a positive real variable. These two determining properties are that any positive-integer power of unity equals unity, and the linear first-order differential equation that a positive-integer power function of a real positive variable satisfies, which is implicit in its derivative. These two determining properties of positive-integer power functions of a positive real variable are extended to arbitrary real values of the positive-integer power. The extended linear first-order differential equations and initial conditions are then used to generate the Taylor expansions of those real power functions of a positive real variable around the zero value of the real power; this can be carried out in at least two different ways. Those Taylor expansions converge for every real value of the power and every positive real value of the variable, and are readily reexpressed entirely in terms of the exponential function and its inverse; one thus has closed formulas for all the real power functions of a positive real variable. Logarithms describe arbitrary positive numbers as real powers of a given positive number; they can expressed entirely in terms of the exponential function's inverse. The value of the particular positive constant whose powers yield the exponential function itself is worked out.

**Category:** General Mathematics

[8] **viXra:1909.0439 [pdf]**
*submitted on 2019-09-20 12:25:01*

**Authors:** A.I.Somsikov

**Comments:** 4 Pages. -

The meaning (logical content) of the concept of numbers is revealed. Arithmetic operations are defined.

**Category:** General Mathematics

[7] **viXra:1909.0421 [pdf]**
*submitted on 2019-09-19 07:58:13*

**Authors:** Viola Maria Grazia

**Comments:** Pages. Successions are successions with positive terms

In this pdf there is my point of view about successions and series. I talk about when a succession (and so a serie) is said convergent making attention to the succession's definition.

**Category:** General Mathematics

[6] **viXra:1909.0359 [pdf]**
*submitted on 2019-09-18 06:27:24*

**Authors:** J Gerard Wolff

**Comments:** 61 Pages. Accepted for publication in the journal "Complexity", 2019-09-17.

This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about 'information compression (IC) via the matching and unification of patterns' (ICMUP. That is itself a novel approach to IC, couched in terms of non-mathematical primitives, as is necessary in any investigation of the foundations of mathematics. This new perspective on the foundations of mathematics reects the idea that, as an aid to human thinking, mathematics is likely to be consonant with much evidence for the importance of IC in human learning, perception, and cognition. This perspective on the foundations of mathematics has grown out of a long-term programme of research developing the SP Theory of Intelligence and its realisation in the SP Computer Model, a system in which a generalised version of ICMUP -- the powerful concept of SP-multiple-alignment -- plays a central role. The paper shows with an example
how mathematics, without any special provision, may achieve compression of information. Then it describes examples showing how variants of ICMUP
may be seen in widely-used structures and operations in mathematics. Examples are also given to show how several aspects of the mathematics-related disciplines of logic and computing may be understood as ICMUP. Also discussed is the intimate relation between IC and concepts of probability, witharguments that there are advantages in approaching AI, cognitive science,
and concepts of probability via ICMUP. Also discussed is how the close relation between IC and concepts of probability relates to the established view that some parts of mathematics are intrinsically probabilistic, and how that latter view may be reconciled with the all-or-nothing, 'exact', forms of calculation or inference that are familiar in mathematics and logic. There are
many potential benefits and applications of the mathematics-as-IC perspective.

**Category:** General Mathematics

[5] **viXra:1909.0330 [pdf]**
*submitted on 2019-09-15 08:15:06*

**Authors:** Louiz Akram

**Comments:** 1 Page.

I present my contribustion in three Claymath Millenium problems.

**Category:** General Mathematics

[4] **viXra:1909.0288 [pdf]**
*submitted on 2019-09-13 12:22:55*

**Authors:** Suraj Deshmukh

**Comments:** 2 Pages.

In this paper I have defined primes on the basis of "skip function" which basically is nothing but tells you how many numbers are skipped between two numbers. And we define a collection of set which I call skip set. The occurrence of a number decides weather it is prime or not.

**Category:** General Mathematics

[3] **viXra:1909.0283 [pdf]**
*submitted on 2019-09-14 00:46:51*

**Authors:** A.I.Somsikov

**Comments:** 4 Pages. -

Definition is given to concepts of number and arithmetic action.

**Category:** General Mathematics

[2] **viXra:1909.0215 [pdf]**
*submitted on 2019-09-09 08:08:04*

**Authors:** Zeolla Gabriel Martín

**Comments:** 25 Pages.

The Simple Tesla algorithm, is the art of multiplying by adding.
We can use this method to calculate the product of any number with true accuracy. It has indisputable applications in various areas such as polynomials, complex numbers, binary numbers and many more.
Basically multiplying is an act of repeated sums, and true to this concept is how this algorithm is developed.

**Category:** General Mathematics

[1] **viXra:1909.0080 [pdf]**
*replaced on 2019-09-18 22:02:27*

**Authors:** Toshiro Takami

**Comments:** 4 Pages.

tan(π)=0, 0 =1, 1 =z =0 2000
When I saw this expression, I was surely suspicious.
But I knew intuitively that Next infinity is zero.
For me, infinite and zero were equal, that’s true now.
The universe did not start with the Big Burn. The universe has existed for an infinite
amount of time, and has repeated an infinite number of big burns.
In other words, the universe is a repetition of Next infinity is zero.

**Category:** General Mathematics